A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle
A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle
复制标题
使用极值原理的“速率无关相变”的变分公式
DOI：
10.1007/s002050200194
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发表时间：
2002
影响因子：
2.5
通讯作者：
V. Levitas
中科院分区：
文献类型：
--
作者：
A. Mielke;F. Theil;V. Levitas
摘要：我们提出了一种与速率无关的形状记忆合金相变滞后演化的介观模型。该模型以变形函数和相位指示函数为基本未知量，以弹性能势和耗散势为本构律。利用相关泛函，可容许过程被定义为在任何时候都是稳定的且满足能量不等式的过程。这个概念导致了一种自然的时间增量方法，它包含在最小化问题中。介观模型是通过松弛过程得到的。它导致了涉及弹性存储能量密度的交叉拟象化的新泛函。对于涉及两相线性化弹性材料的特殊情况，我们证明了当时间步长趋近于0时，增量问题提供了时间连续问题的可容许过程的存在性。
Abstract We propose a rate-independent, mesoscopic model for the hysteretic evolution of phase transformations in shape-memory alloys. The model uses the deformation and phase-indicator function as basic unknowns and the potentials for the elastic energy and for the dissipation as constitutive laws. Using the associated functionals, admissible processes are defined to be the ones which are stable at all times and which satisfy the energy inequality.This concept leads to a natural time-incremental method which consists in a minimization problem. The mesoscopic model is obtained by a relaxation procedure. It leads to new functionals involving the cross-quasiconvexification of the elastic stored-energy density. For a special case involving two phases of linearized elastic materials we show that the incremental problem provides existence of admissible processes for the time-continuous problem, if we let the time-step go to 0.
Dedicated to Erwin Stein on the occasion of his seventieth
birthday